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30 September, 16:26

A boat leaves a dock at 6:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 7:00 PM How many minutes after 6:00 PM were the two boats closest together

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  1. 30 September, 16:51
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    22 minutes

    Explanation:

    Let t be the time after 6 PM.

    D be the distance

    During time t, the First boat travelling south = 20t km.

    Meanwhile, the second boat travelling east is = 15t km,

    Then the second boat started 15 km from the dock, so the distance from the dock is = (15 - 15t) km.

    The distance D between the two boats is is expressed as = (15 - 15t) ^2 + (20t) ^2 = D*2

    Let differentiate with respect to time and making dD/dt to 0 (D minimization is important),

    then 2 (15 - 15t) (-15) + 2 (20t) (20) = 0

    Therefore t = 9/25 h or 0.36 h or 22 minutes
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